WASHINGTON — In a new twist to a widening tale of ethical lapses in the military, the Navy is investigating cheating allegations against about one-fifth of its trainers at a school for naval nuclear power reactor operators.

It is the second exam-cheating scandal to hit the military this year, on top of a series of disclosures in recent months of ethical lapses at all ranks in the military as it transitions from more than a decade of war-fighting.

Unlike an Air Force cheating probe that has implicated nearly 100 officers responsible for land-based nuclear missiles that stand ready for short-notice launch, those implicated in the Navy investigation have no responsibility for nuclear weapons.

The Air Force probe is centered on Malmstrom Air Force Base, Mont., but could spread to its two other nuclear missile bases in North Dakota and Wyoming. Dozens of officers at Malmstrom have been linked to cheating on a monthly test of their proficiency in handling “emergency war orders” for potential launch of nuclear missiles.

The Navy said its implicated sailors are accused of having cheated on written tests they must pass to be certified as instructors at a nuclear propulsion school at Charleston, SC. The Navy uses two nuclear reactors there to train sailors for duty aboard any of dozens of submarines and aircraft carriers around the world whose onboard reactors provide propulsion. They are not part of any weapons systems.

The accused sailors had previously undergone reactor operations training at Charleston before deploying aboard a nuclear-power vessel. In the normal course of career moves, they returned to Charleston to serve as instructors, for which they have to pass requalification exams.

Adm. John Richardson, director of the Navy’s nuclear propulsion program, said an undisclosed number of senior sailors are alleged to have provided test information to their peers. He was not more specific, but one official said the information was shared from the sailors’ home computers, which could be a violation of security rules because information about nuclear reactors operations is classified.

“That’ll be an active part of the investigation to fully understand” the extent of any security rule violations, Richardson said. He said the last time the Navy had such a cheating scandal involving its nuclear reactor operators was in 2010 when the USS Memphis, a nuclear-powered submarine, lost about 10 percent of its crew to disciplinary measures after a cheating ring was discovered.

Richardson said the alleged cheating at Charleston came to light Monday when a senior enlisted sailor at the training site reported it to higher authorities. Richardson said the unidentified sailor “recognized that this was wrong” and chose to report it.

The matter was still under investigation by the Naval Criminal Investigative Service.

Adm. Jonathan Greenert, the chief of naval operations, said at a joint announcement with Richardson that he was upset to learn of the breakdown in discipline.

Neither Greenert nor Richardson identified the rank of the alleged cheaters but described them as senior enlisted members. There are about 150 nuclear power reactor instructors at the Charleston site. With about 30 of them banned, at least temporarily, from performing their duties, the training program might suffer.

“I could possibly foresee an impact in Charleston,” Richardson said. “We’ll see if that is broader.”

Pressed to say how many sailors were implicated in the investigation, Richardson said a “ballpark figure” was something like 12 to 20. But a short time later, another Navy official said the number was approximately 30 but could change as the investigation unfolds. The official spoke on condition of anonymity because the official was not authorized to discuss publicly any details beyond what Richardson and Greenert disclosed at their news conference.

Richardson said he could not discuss possible disciplinary action against those involved because the probe was ongoing. However, he said anyone in the naval nuclear power program — either in a training setting or aboard a ship at sea — who is caught cheating would usually be removed from the program and “generally” would be kicked out of the Navy.

The decision to have Greenert and Richardson announce the cheating investigation publicly was a sign of how seriously the Navy takes the matter.